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Display information for equation id:math.2033.48 on revision:2033
* Page found: Vektorfelder als dynamische Systeme (eq math.2033.48)
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Hash: 08afe5b8dd4f373b858174def63f1e09
TeX (original user input):
\begin{align}
& \det (A-\lambda 1)=0\Rightarrow \left| \left( \begin{matrix}
-\lambda & \frac{1}{m{{l}^{2}}} \\
-mgl & -\lambda -2\gamma \\
\end{matrix} \right) \right|=0={{\lambda }^{2}}+2\gamma \lambda +\frac{g}{l} \\
& \frac{g}{l}={{\omega }^{2}} \\
\end{align}
TeX (checked):
{\begin{aligned}&\det(A-\lambda 1)=0\Rightarrow \left|\left({\begin{matrix}-\lambda &{\frac {1}{m{{l}^{2}}}}\\-mgl&-\lambda -2\gamma \\\end{matrix}}\right)\right|=0={{\lambda }^{2}}+2\gamma \lambda +{\frac {g}{l}}\\&{\frac {g}{l}}={{\omega }^{2}}\\\end{aligned}}
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MathML (1.978 KB / 469 B) :
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd></mtd><mtd><mi>det</mi><mo>⁡</mo><mo stretchy="false">(</mo><mi>A</mi><mo>−</mo><mi>λ</mi><mn>1</mn><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn><mo>⇒</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mtable columnspacing="1em" rowspacing="4pt"><mtr><mtd><mo>−</mo><mi>λ</mi></mtd><mtd><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>m</mi><msup><mi>l</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mrow></mfrac></mrow></mtd></mtr><mtr><mtd><mo>−</mo><mi>m</mi><mi>g</mi><mi>l</mi></mtd><mtd><mo>−</mo><mi>λ</mi><mo>−</mo><mn>2</mn><mi>γ</mi></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">|</mo></mrow><mo>=</mo><mn>0</mn><mo>=</mo><msup><mi>λ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>+</mo><mn>2</mn><mi>γ</mi><mi>λ</mi><mo>+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>g</mi></mrow><mrow data-mjx-texclass="ORD"><mi>l</mi></mrow></mfrac></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>g</mi></mrow><mrow data-mjx-texclass="ORD"><mi>l</mi></mrow></mfrac></mrow><mo>=</mo><msup><mi>ω</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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